The Color Theory is the theory that each Link's theme color indicates how much/how often Link's personality tends to draw from the traits of each Link. That is, the closer a Link's theme color is to green (or a cool color in general), the more his traits tend to manifest in Link. Why the color green? Well, simply put, it's the color he always wears. Perhaps the Four Sword prioritizes the traits most often seen in the person to receive the color that person typically wears.
The proposed order of Links from "most prominent in Link" to "least prominent in Link" is Green, Blue, Vio, and Red. This is not to say that Green is the "most important" or that Red "isn't really present in Link". This simply means that when looking at Link as a whole and how he typically acts, we tend to see traits embodied by Green the most often, followed by traits embodied by Blue, etc. I believe this order is accurate given how often most fans mistake Green as a one-to-one copy of Link and how they tend to see Vio more as his own person than simply a part of Link. Indeed, a person who is not too invested in the work would probably say that Link's behavior at the beginning of the story mirrors Green and Blue most, followed by Vio and then Red.
Non-exhaustive examples of what I mean about the Links' traits manifesting in Link:
Naturally, because every Link is a valid version of Link in the end, there are many moments where Link is present that you could argue multiple Links' traits are manifesting (or that "multiple Links would do that". Even the examples listed above can be disputed, and if I tried to list out the moments where it seems like all four Links would perform Link's actions, it would be too long. Regardless, we will operate under the assumption that Green is the most "prototypical Link" (that is, he resembles the original Link most often), as outlined by Akira Himekawa in the Legendary Edition concept sketches. From here, we can reason through the order of Green to Red mentioned above and then tie this into Link's personality.
Green's theme color is green, so he occupies the first spot in the progression. From here, we move on to Blue, as blue is one of the component colors of green but is not combined with any warm colors. As a reminder, in this theory, warm colors and lacking the two color components of the color green lessen a Link's influence on Link's personality. Thus, Vio is next because purple is composed of blue and red - a component of the color green and a warm color. Finally, Red is last because his theme color is solely a warm color which also happens to not be a component of the color green at all.
If we apply this order to the traits that the Links represent, it seems to align with what we see of Link in canon: for the most part, he is a hot-blooded person who is also sometimes hotheaded, less often cool and collected, and more rarely overtly optimistic. This is based on what Vio assigns to the Links in chapter 2, though if I can add my own very brief and simplified descriptions of the Links in with this, I would say Link is a caring person (Green) who is sometimes overconfident (Blue) but can be serious when he needs to be (Vio) and sometimes gets into mischief or lets his curiosity drive him (Red).
There is certaintly no actual canonical evidence for this theory. I just thought of it one day and thought it was fun and neat. It gets to have its home here now.